Lattice mechanical properties of yttrium and scandium

Abstract

Our previous three-body force model [8] is modified and used to calculate the elastic constants and phonon dispersion curves of yttrium and scandium. It is demonstrated that the interpretation of the volume strain as the local strain, as the adiabatic hypothesis demands, leads to an effective three-body interaction which is essential to guarantee the equality of the static and dynamic elastic constants. This model satisfies the two equilibrium conditions and the symmetry properties of the dynamical matrix. The results obtained with this model are in good agreement with the available experimental data. The experimental phonon dispersion curves for these metals do not provide a clear picture along the [1 1 2 0] direction. Out of the six possible branches only two are measured; the other four which would provide valuable informations about the importance of three-body forces are not available. As for these branches, the calculated results may provide useful information.